/* ----------------------------------------------------------------------  
* Copyright (C) 2010 ARM Limited. All rights reserved.  
*  
* $Date:        29. November 2010  
* $Revision: 	V1.0.3  
*  
* Project: 	    CMSIS DSP Library  
* Title:	    arm_biquad_cascade_df1_f32.c  
*  
* Description:	Processing function for the  
*               floating-point Biquad cascade DirectFormI(DF1) filter.  
*  
* Target Processor: Cortex-M4/Cortex-M3
*  
* Version 1.0.3 2010/11/29 
*    Re-organized the CMSIS folders and updated documentation.  
*   
* Version 1.0.2 2010/11/11  
*    Documentation updated.   
*  
* Version 1.0.1 2010/10/05   
*    Production release and review comments incorporated.  
*  
* Version 1.0.0 2010/09/20   
*    Production release and review comments incorporated.  
*  
* Version 0.0.5  2010/04/26   
* 	 incorporated review comments and updated with latest CMSIS layer  
*  
* Version 0.0.3  2010/03/10   
*    Initial version  
* -------------------------------------------------------------------- */ 
 
#include "arm_math.h" 
 
/**  
 * @ingroup groupFilters  
 */ 
 
/**  
 * @defgroup BiquadCascadeDF1 Biquad Cascade IIR Filters Using Direct Form I Structure  
 *  
 * This set of functions implements arbitrary order recursive (IIR) filters.  
 * The filters are implemented as a cascade of second order Biquad sections.  
 * The functions support Q15, Q31 and floating-point data types. Fast version of Q15 and Q31 also supported.  
 *  
 * The functions operate on blocks of input and output data and each call to the function  
 * processes <code>blockSize</code> samples through the filter.  
 * <code>pSrc</code> points to the array of input data and  
 * <code>pDst</code> points to the array of output data.  
 * Both arrays contain <code>blockSize</code> values.  
 *  
 * \par Algorithm  
 * Each Biquad stage implements a second order filter using the difference equation:  
 * <pre>  
 *     y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]  
 * </pre>  
 * A Direct Form I algorithm is used with 5 coefficients and 4 state variables per stage.  
 * \image html Biquad.gif "Single Biquad filter stage"  
 * Coefficients <code>b0, b1 and b2 </code> multiply the input signal <code>x[n]</code> and are referred to as the feedforward coefficients.  
 * Coefficients <code>a1</code> and <code>a2</code> multiply the output signal <code>y[n]</code> and are referred to as the feedback coefficients.  
 * Pay careful attention to the sign of the feedback coefficients.  
 * Some design tools use the difference equation  
 * <pre>  
 *     y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] - a1 * y[n-1] - a2 * y[n-2]  
 * </pre>  
 * In this case the feedback coefficients <code>a1</code> and <code>a2</code> must be negated when used with the CMSIS DSP Library.  
 *  
 * \par  
 * Higher order filters are realized as a cascade of second order sections.  
 * <code>numStages</code> refers to the number of second order stages used.  
 * For example, an 8th order filter would be realized with <code>numStages=4</code> second order stages.  
 * \image html BiquadCascade.gif "8th order filter using a cascade of Biquad stages"  
 * A 9th order filter would be realized with <code>numStages=5</code> second order stages with the coefficients for one of the stages configured as a first order filter (<code>b2=0</code> and <code>a2=0</code>).  
 *  
 * \par  
 * The <code>pState</code> points to state variables array.  
 * Each Biquad stage has 4 state variables <code>x[n-1], x[n-2], y[n-1],</code> and <code>y[n-2]</code>.  
 * The state variables are arranged in the <code>pState</code> array as:  
 * <pre>  
 *     {x[n-1], x[n-2], y[n-1], y[n-2]}  
 * </pre>  
 *  
 * \par  
 * The 4 state variables for stage 1 are first, then the 4 state variables for stage 2, and so on.  
 * The state array has a total length of <code>4*numStages</code> values.  
 * The state variables are updated after each block of data is processed, the coefficients are untouched.  
 *  
 * \par Instance Structure  
 * The coefficients and state variables for a filter are stored together in an instance data structure.  
 * A separate instance structure must be defined for each filter.  
 * Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.  
 * There are separate instance structure declarations for each of the 3 supported data types.  
 *  
 * \par Init Functions  
 * There is also an associated initialization function for each data type.  
 * The initialization function performs following operations:  
 * - Sets the values of the internal structure fields.  
 * - Zeros out the values in the state buffer.  
 *  
 * \par  
 * Use of the initialization function is optional.  
 * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.  
 * To place an instance structure into a const data section, the instance structure must be manually initialized.  
 * Set the values in the state buffer to zeros before static initialization.  
 * The code below statically initializes each of the 3 different data type filter instance structures  
 * <pre>  
 *     arm_biquad_casd_df1_inst_f32 S1 = {numStages, pState, pCoeffs};  
 *     arm_biquad_casd_df1_inst_q15 S2 = {numStages, pState, pCoeffs, postShift};  
 *     arm_biquad_casd_df1_inst_q31 S3 = {numStages, pState, pCoeffs, postShift};  
 * </pre>  
 * where <code>numStages</code> is the number of Biquad stages in the filter; <code>pState</code> is the address of the state buffer;  
 * <code>pCoeffs</code> is the address of the coefficient buffer; <code>postShift</code> shift to be applied.  
 *  
 * \par Fixed-Point Behavior  
 * Care must be taken when using the Q15 and Q31 versions of the Biquad Cascade filter functions.  
 * Following issues must be considered:  
 * - Scaling of coefficients  
 * - Filter gain  
 * - Overflow and saturation  
 *  
 * \par  
 * <b>Scaling of coefficients: </b>  
 * Filter coefficients are represented as fractional values and  
 * coefficients are restricted to lie in the range <code>[-1 +1)</code>.  
 * The fixed-point functions have an additional scaling parameter <code>postShift</code>  
 * which allow the filter coefficients to exceed the range <code>[+1 -1)</code>.  
 * At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.  
 * \image html BiquadPostshift.gif "Fixed-point Biquad with shift by postShift bits after accumulator"  
 * This essentially scales the filter coefficients by <code>2^postShift</code>.  
 * For example, to realize the coefficients  
 * <pre>  
 *    {1.5, -0.8, 1.2, 1.6, -0.9}  
 * </pre>  
 * set the pCoeffs array to:  
 * <pre>  
 *    {0.75, -0.4, 0.6, 0.8, -0.45}  
 * </pre>  
 * and set <code>postShift=1</code>  
 *  
 * \par  
 * <b>Filter gain: </b>  
 * The frequency response of a Biquad filter is a function of its coefficients.  
 * It is possible for the gain through the filter to exceed 1.0 meaning that the filter increases the amplitude of certain frequencies.  
 * This means that an input signal with amplitude < 1.0 may result in an output > 1.0 and these are saturated or overflowed based on the implementation of the filter.  
 * To avoid this behavior the filter needs to be scaled down such that its peak gain < 1.0 or the input signal must be scaled down so that the combination of input and filter are never overflowed.  
 *  
 * \par  
 * <b>Overflow and saturation: </b>  
 * For Q15 and Q31 versions, it is described separately as part of the function specific documentation below.  
 */ 
 
/**  
 * @addtogroup BiquadCascadeDF1  
 * @{  
 */ 
 
/**  
 * @param[in]  *S         points to an instance of the floating-point Biquad cascade structure.  
 * @param[in]  *pSrc      points to the block of input data.  
 * @param[out] *pDst      points to the block of output data.  
 * @param[in]  blockSize  number of samples to process per call.  
 * @return     none.  
 *  
 */ 
 
void arm_biquad_cascade_df1_f32( 
  const arm_biquad_casd_df1_inst_f32 * S, 
  float32_t * pSrc, 
  float32_t * pDst, 
  uint32_t blockSize) 
{ 
  float32_t *pIn = pSrc;                         /*  source pointer            */ 
  float32_t *pOut = pDst;                        /*  destination pointer       */ 
  float32_t *pState = S->pState;                 /*  pState pointer            */ 
  float32_t *pCoeffs = S->pCoeffs;               /*  coefficient pointer       */ 
  float32_t acc;                                 /*  Simulates the accumulator */ 
  float32_t b0, b1, b2, a1, a2;                  /*  Filter coefficients       */ 
  float32_t Xn1, Xn2, Yn1, Yn2;                  /*  Filter pState variables   */ 
  float32_t Xn;                                  /*  temporary input           */ 
  uint32_t sample, stage = S->numStages;         /*  loop counters             */ 
 
 
  do 
  { 
    /* Reading the coefficients */ 
    b0 = *pCoeffs++; 
    b1 = *pCoeffs++; 
    b2 = *pCoeffs++; 
    a1 = *pCoeffs++; 
    a2 = *pCoeffs++; 
 
    /* Reading the pState values */ 
    Xn1 = pState[0]; 
    Xn2 = pState[1]; 
    Yn1 = pState[2]; 
    Yn2 = pState[3]; 
 
    /* Apply loop unrolling and compute 4 output values simultaneously. */ 
    /*      The variable acc hold output values that are being computed:  
     *  
     *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]  
     *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]  
     *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]  
     *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]  
     */ 
 
    sample = blockSize >> 2u; 
 
    /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.  
     ** a second loop below computes the remaining 1 to 3 samples. */ 
    while(sample > 0u) 
    { 
      /* Read the first input */ 
      Xn = *pIn++; 
 
      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ 
      Yn2 = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2); 
 
      /* Store the result in the accumulator in the destination buffer. */ 
      *pOut++ = Yn2; 
 
      /* Every time after the output is computed state should be updated. */ 
      /* The states should be updated as:  */ 
      /* Xn2 = Xn1    */ 
      /* Xn1 = Xn     */ 
      /* Yn2 = Yn1    */ 
      /* Yn1 = acc   */ 
 
      /* Read the second input */ 
      Xn2 = *pIn++; 
 
      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ 
      Yn1 = (b0 * Xn2) + (b1 * Xn) + (b2 * Xn1) + (a1 * Yn2) + (a2 * Yn1); 
 
      /* Store the result in the accumulator in the destination buffer. */ 
      *pOut++ = Yn1; 
 
      /* Every time after the output is computed state should be updated. */ 
      /* The states should be updated as:  */ 
      /* Xn2 = Xn1    */ 
      /* Xn1 = Xn     */ 
      /* Yn2 = Yn1    */ 
      /* Yn1 = acc   */ 
 
      /* Read the third input */ 
      Xn1 = *pIn++; 
 
      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ 
      Yn2 = (b0 * Xn1) + (b1 * Xn2) + (b2 * Xn) + (a1 * Yn1) + (a2 * Yn2); 
 
      /* Store the result in the accumulator in the destination buffer. */ 
      *pOut++ = Yn2; 
 
      /* Every time after the output is computed state should be updated. */ 
      /* The states should be updated as: */ 
      /* Xn2 = Xn1    */ 
      /* Xn1 = Xn     */ 
      /* Yn2 = Yn1    */ 
      /* Yn1 = acc   */ 
 
      /* Read the forth input */ 
      Xn = *pIn++; 
 
      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ 
      Yn1 = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn2) + (a2 * Yn1); 
 
      /* Store the result in the accumulator in the destination buffer. */ 
      *pOut++ = Yn1; 
 
      /* Every time after the output is computed state should be updated. */ 
      /* The states should be updated as:  */ 
      /* Xn2 = Xn1    */ 
      /* Xn1 = Xn     */ 
      /* Yn2 = Yn1    */ 
      /* Yn1 = acc   */ 
      Xn2 = Xn1; 
      Xn1 = Xn; 
 
      /* decrement the loop counter */ 
      sample--; 
 
    } 
 
    /* If the blockSize is not a multiple of 4, compute any remaining output samples here.  
     ** No loop unrolling is used. */ 
    sample = blockSize & 0x3u; 
 
    while(sample > 0u) 
    { 
      /* Read the input */ 
      Xn = *pIn++; 
 
      /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ 
      acc = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2); 
 
      /* Store the result in the accumulator in the destination buffer. */ 
      *pOut++ = acc; 
 
      /* Every time after the output is computed state should be updated. */ 
      /* The states should be updated as:    */ 
      /* Xn2 = Xn1    */ 
      /* Xn1 = Xn     */ 
      /* Yn2 = Yn1    */ 
      /* Yn1 = acc   */ 
      Xn2 = Xn1; 
      Xn1 = Xn; 
      Yn2 = Yn1; 
      Yn1 = acc; 
 
      /* decrement the loop counter */ 
      sample--; 
 
    } 
 
    /*  Store the updated state variables back into the pState array */ 
    *pState++ = Xn1; 
    *pState++ = Xn2; 
    *pState++ = Yn1; 
    *pState++ = Yn2; 
 
    /*  The first stage goes from the input wire to the output wire. */ 
    /*  Subsequent numStages occur in-place in the output wire */ 
    pIn = pDst; 
 
    /* Reset the output pointer */ 
    pOut = pDst; 
 
    /* decrement the loop counter */ 
    stage--; 
 
  } while(stage > 0u); 
 
} 
 
 
  /**  
   * @} end of BiquadCascadeDF1 group  
   */ 
